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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 20, Iss. 2 — Jan. 15, 1981
  • pp: 307–311

Precision of ellipsometer nulling

U. Merkt  »View Author Affiliations


Applied Optics, Vol. 20, Issue 2, pp. 307-311 (1981)
http://dx.doi.org/10.1364/AO.20.000307


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Abstract

A least squares method for the precise nulling of an arbitrary ellipsometer arrangement is presented, and the standard errors of the null settings are calculated. The general expressions obtained are applied to the most common null ellipsometers, i.e., the PCSA and PSCA arrangements. For these ellipsometers we arrive at simple closed formulas that show the influence of the noise of the detected light, the extinction ratio of the ellipsometer, and the reflectivity and ellipsometric angles of the sample. In addition, coupling is discussed. It is shown, especially for the PSCA ellipsometer, that coupling has little effect on precision if the least squares method is used.

© 1981 Optical Society of America

History
Original Manuscript: June 21, 1980
Published: January 15, 1981

Citation
U. Merkt, "Precision of ellipsometer nulling," Appl. Opt. 20, 307-311 (1981)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-20-2-307


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References

  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  2. G. Wedler, Chemisorption—An Experimental Approach (Butterworths, London, 1976), p. 89.
  3. U. Merkt, P. Wissmann, Thin Solid Films 57, 65 (1979); Z. Phys. Chem. Frankfurt am Main 115, 55 (1979); Surf. Sci. 96, 529 (1980). [CrossRef]
  4. E. Schmidt, J. Opt. Soc. Am. 60, 490 (1970). The last three lines of Eq. (1) in this reference should read 0.5RsRp sin2A{cosΔ sin2Q cos2(P-Q)+sin2(P-Q) [cos2Q cos(θ+Δ)-sin2Q cos(θ-Δ)]}. [CrossRef]
  5. D. E. As’pnes, Appl. Opt. 14, 1131 (1975). [CrossRef] [PubMed]
  6. D. L. Confer, R. M. A. Azzam, N. M. Bashara, Appl. Opt. 15, 2568 (1976). [CrossRef] [PubMed]
  7. M. P. Kothiyal, Appl. Opt. 18, 1019 (1979). [CrossRef] [PubMed]
  8. As unit for plane angle degree used in the text but radian in the equations.
  9. E. V. Haynsworth, K. Goldberg, in Handbook of Mathematical Functions, M. Abramowitz, I. A. Stegun, Eds. (Dover, New York, 1965), p. 804.
  10. U. Merkt, Dissertation, U. Erlangen-Nürnberg, 1978.
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 43.
  12. In the PCSA arrangement ψi is given by cos2ψi = −cos2C cos2(P − C).
  13. Ref. 5, Eq. (13).
  14. Ref. 1, p. 385.
  15. The coefficients for the PCSA (Cfixed = arbitrary) ellipsometer can be derived from Eq. (1) in Ref. 4. The results, omitting a common constant 2rI0, are a = sin2ψ cos2A0 + cos2ψ sin2A0, b = sin2ψ sin2C + cos2ψ cos2C − cos2 (P0 − C) cos2C cos2ψ, and c = sin2(P0 − C) sin2A0 cos2C − cos2A0 sin2ψ cos2(P0 − C) sinΔ cos22C. The null settings of the polarizer P0 and analyzer A0 can be calculated using Eqs. (2) and (3) in Ref. 4. With the given coefficients the standard errors can be determined according to Eq. (7) of this paper.
  16. A. Rothen, General Theory and Operating Instructions for the Ellipsometer (Rudolph Research, Fairfield, Conn.1958).
  17. H. G. Jerrard, J. Opt. Soc. Am. 42, 159 (1952). [CrossRef]
  18. G. Szivessy, in Handbuch der Physik, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1928), Vol. 19, Chap. 28, p. 924, Eq. (30).
  19. For an arbitrary ellipsometer the number of steps necessary to null it is n = 1 + ln(∑/σ)/ln(4ab/c2) for each adjustable component.

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